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A235648 Perimeter (rounded down) of a tetraflake-like fractal after n iterations, a(1) = 1 (see comments).

%I A235648 #14 Feb 16 2025 08:33:21
%S A235648 1,1,2,3,4,7,10,16,25,39,61,97,155,249,404,657,1073,1759,2892,4768,
%T A235648 7877,13036,21602,35838,59508,98885,164416,273502,455137,757628,
%U A235648 1261470,2100791,3499106,5828894,9710891,16179575,26958966,44922289,74858052,124746848,207889317
%N A235648 Perimeter (rounded down) of a tetraflake-like fractal after n iterations, a(1) = 1 (see comments).
%C A235648 Construction rule is same as for box and Vicsek fractals, but uses 6 boxes at initial stage (n = 1) and has only one symmetrical axis. The scale factor of these fractals is 1/3. The actual tetraflake fractals have a scale factor of 1/2.
%C A235648 The total number of sides at different lengths of a tetraflake-like fractal after n iterations is A235643(n). The total number of holes is A241271(n+1).
%H A235648 Kival Ngaokrajang, <a href="/A235648/a235648.pdf">Illustration of initial terms</a>
%H A235648 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BoxFractal.html">Box Fractal</a>
%H A235648 Wikipedia, <a href="http://en.wikipedia.org/wiki/N-flake">n-flake</a>
%H A235648 Wikipedia, <a href="http://en.wikipedia.org/wiki/Vicsek_fractal">Vicsek Fractal</a>
%F A235648 Floor((5*a(n-1)-2*(4*c(n-1)+3^(n-1)))/18) for n >1, a(1)=18, c(1)=1.
%o A235648 (PARI){a=18;c=1;print1(1,", "); for (n=1,50, c=4*c+3^(n-1); a=5*a-2*c; aa=floor((a*(1/3)^n)/18); print1(aa,", "));}
%Y A235648 Cf. A241271, A235643.
%Y A235648 Cf. A240523 (pentaflake), A240671 (heptaflake), A240572 (octaflake), A240733 (nonaflake), A240734 (decaflake), A240840 (hendecaflake), A240735 (dodecaflake), A240841 (tridecaflake).
%Y A235648 Cf. A063628 (hexaflake).
%Y A235648 Cf. A240916, A240917 (triflake-like); A238777 (tetraflake-like).
%K A235648 nonn
%O A235648 1,3
%A A235648 _Kival Ngaokrajang_, Apr 20 2014